Acoustic surface diffusers are well known for use in scattering or diffusing sound reflections. Such devices are used to alter the acoustics of an environment. When arranging multiple diffusers on a surface such as a wall, it is a common practice to employ a periodic array. In other words, a pattern of recesses or protrusions is arranged to repeat itself over and over again across the surface being treated. Such a practice is widely acceptable from a visual perspective and is advantageous in that it reduces manufacturing costs. Unfortunately, periodic repetition of a series of acoustic features such as wells or protrusions often reduces the effectiveness of diffusion and/or scattering and, consequently, the ability of the diffusing surface to disperse sound. Thus, a need has developed for an acoustical diffusor system that avoids the deficiencies of the use of repetitive periodic arrays of diffusing elements.
If a scattering surface is made so that an array is periodic, i.e., having many repeats of a single base shape, then there will be directions where scattered energy lobes form due to constructive interference between identical parts of the repeated base shapes. In the example of scattering in a single plane with normal incident plane waves, for many audible frequencies, repetition lobes dominate the scattered energy polar response. This can mean that the scattered energy is concentrated in only a few directions, resulting in uneven coverage and less than complete diffusion. In this regard, the far field scattered energy is independent of scattering angle. In a simple example of a base shape having a width W, and the wavelength of sound is xcex, then the repetition lobes will be in the directions xcex8 according to the formula xcex8=sinxe2x88x921 (mxcex/W), where m is an integer with |mxcex/W|xe2x89xa61.
One solution to the problem of periodicity is to increase the repeat length W while still maintaining some periodicity as this will generate more scattering lobes and therefore make diffusion more complete. This is generally an expensive approach since the large base shape is more expensive to fabricate or mold. Another more effective solution is to remove periodicity altogether, while manufacturing a relatively small asymmetric shape.
While one solution to the issue of periodicity is to make a surface having no repeats, this is often not an effective solution because (1) periodicity is often a visual requirement of the customer, and (2) manufacturing costs become prohibitive. Angus suggested the use of modulation using two different base shapes of Schroeder diffusors, where the first base shape is denoted A, and the second base shape is denoted B. Angus suggested that the base shapes A and B could be arranged in random order on a wall surface, for example, in the pattern A A A B A (J. A. Angus xe2x80x9cUsing Modulated Phase Reflection Gratings to Achieve Specific Diffusion Characteristicsxe2x80x9d presented at the 99th Audio Engineering Society Convention, pre-print 4117 (October, 1995)).
Such a solution reduces or removes periodicity effects but still often results in a shape which is random and difficult to visually decode. In addition, if a solution could be obtained using only a single base shape, manufacturing costs would be drastically reduced over the manufacturing costs that would be required to implement the concept disclosed by Angus.
The present invention relates to embodiments of aperiodic tiling of a single asymmetrical diffusive base shape or module. The present invention includes the following interrelated objects, aspects and features:
(1) In accordance with the teachings of the present invention, Applicants have found that by forming an aperiodic arrangement, sequence or array of diffusors, or by increasing repeat unit length, the effects of periodicity can be removed or reduced. We are describing two diffusorsxe2x80x94an asymmetrical base shape and an extended arrangement of this base shape in two or three dimensions and in diverse orientations forming a larger aperiodic diffusor having minimal scattered energy lobing. In the past, multiple Schroeder diffusor base shapes have been arranged to form an aperiodic array. The present invention seeks to improve upon that technique by providing other ways of achieving an aperiodic tiled array using a single asymmetrical base shape which is either a welled or stepped one-dimensional or two-dimensional diffusor, a single or compound curved surface, or an aperiodic geometrical form.
(2) Surfaces such as those described in paragraph (1) above can be tiled in any orientation offering an unlimited number of tiling patterns. In the preferred embodiments of the present invention, a smooth transition between adjacent xe2x80x9ctilesxe2x80x9d is achieved because the perimeter of each tile is provided with a specific depth and zero gradient whereby when adjacent tiles are placed in adjacency, there is a smooth transition between the adjacent tiles. For example, where the diffusor is a one-dimensional diffusor, a half well is provided at each end thereof which precisely matches a half well formed on the adjacent tile. In this way, two adjacent half wells create a single well, thereby providing a continuity in transition between adjacent tiles. Application of this principle to two-dimensional diffusers, single or compound curved surfaces or aperiodic geometric forms will be explained in greater detail hereinafter. However, using a tileable single asymmetric base shape reduces the number of shapes requiring manufacture while allowing modulation. The present invention even contemplates extending the techniques thereof into three-dimensional shapes to form volume diffusors.
(3) An asymmetrical welled diffusor base shape or module can be designed in a variety of ways including use of numerical optimization. As explained above, diffusors can be single plane (one-dimensional) or hemispherical (two-dimensional) as well as other curves and shapes. Whereas prior diffusors have employed the use of number theory sequences, the present invention does not require the use of number theory sequences in determining the pattern of wells in the diffusor. Applicants have shown that use of boundary element and multi-dimensional optimization techniques can be used to design diffusors with better performance than number theory approaches, especially for diffusors with a limited number of wells. Thus, one example of an optimized one-dimensional diffusor usable in accordance with the teachings of the present invention can include eight wells including 7 full wells and a half well at each end. A depth sequence that has been found to be effective in practicing the teachings of the present invention includes a depth sequence equal to or proportional to the following: 0xe2x80x3, 3xe2x80x3, 6{fraction (7/16)}xe2x80x3, 3xe2x85x9exe2x80x3, 5{fraction (1/16)}xe2x80x3, 2{fraction (11/16)}xe2x80x3, 4⅝ and {fraction (13/16)}xe2x80x3.
(4) The technique employed to design aperiodic diffusor sequences to be used in accordance with the teachings of the present invention may rely upon visual appearance, a random sequence, a number theory sequence, or use of an optimization program.
Accordingly, it is a first object of the present invention to provide embodiments of aperiodic tiling of a single asymmetric diffusive base shape or module.
It is a further object of the present invention to provide such a device, in each embodiment, in which a single form of diffusor is conceived, and is arranged in a sequence either as conceived or re-oriented so as to eliminate periodicity.
It is a still further object of the present invention to provide such a device applicable to one-dimensional, two-dimensional and three-dimensional diffusors.
It is a still further object of the present invention to provide such a device applicable to three-dimensional geometrical shapes and simple or compound curves.
It is a yet further object of the present invention to provide such a device in which the perimeter of each tile is specifically designed to provide a smooth transition to adjacent tiles.
It is a yet further object of the present invention to provide such a device in which knowledge of the eventual visual appearance is employed in designing the diffusors to be employed therein.
It is a yet further object of the present invention to design the diffusor sequences randomly, in accordance with a number theory sequence, or through the use of an optimization program.
It is a yet further object of the present invention to provide such a device in which the diffusors are asymmetrical.
These and other objects, aspects and features of the present invention will be better understood from the following detailed description of the preferred embodiments when read in conjunction with the appended drawing figures.